Hasil dari Lim x>1 (x-1)(√x+1)/√x-1 adalah..

Hasil dari Lim x>1 (x-1)(√x+1)/√x-1 adalah..

Penyelesaian:

$displaystyle lim_{x to 1} frac{(x-1)(sqrt{x}+1)}{sqrt{x}-1} times frac{sqrt{x}+1}{sqrt{x}+1} \ = lim_{x to 1} frac{(x-1)(sqrt{x}+1)^2}{left(sqrt{x}right)^2-1^2} \ = lim_{x to 1} frac{(x-1)(sqrt{x}+1)^2}{x-1} \ = lim_{x to 1} (sqrt{x}+1)^2 \ = (sqrt{(1)}+1)^2 \ = (1+1)^2 \ = (2)^2 \ = 4$

Jawaban

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